A self-scaling sequential quasi-Newton method for estimating the heat transfer coefficient distribution in the air jet impingement

Abstract

Accurate knowledge of the heat transfer coefficient (HTC) distribution is of great significance to the control and optimization of the heat transfer system in the air jet impingement. For this purpose, the estimation of the temporally-spatially varying HTC in the air jet impingement is studied based on the inverse heat conduction problem. The transient two-dimensional heat conduction model of the target disc under a single cooling air jet is established and utilized as the direct problem. A self-scaling sequential quasi-Newton method (SS-SQNM) is developed for accurately and efficiently solving the inverse problem. As a modification of the sequential quasi-Newton method (SQNM), the SS-SQNM adopts the self-scaling updating equation to accelerate the single-step convergence rate during iteration, and thus attains higher inversion efficiency than the SQNM. A series of numerical tests are carried out to investigate the performance of the SS-SQNM and the effects of the regularization parameters on inverse results. The results reveal that the SS-SQNM can give stable and accurate estimates of the HTC when regularization parameters are appropriately selected through the discrepancy principle. The mean absolute percentage error of the estimated HTC distribution is generally less than 10.2% in the presence of measurement noises. Additionally, the iteration number required by the SS-SQNM for inversion is only about 7.81%∼27.78% of that of the SQNM under the same conditions, which saves lots of computational time for the SS-SQNM. Therefore, the SS-SQNM developed in this study is a promising inverse algorithm, which can be employed to estimate the HTC distribution in the air jet impingement with reasonable accuracy and efficiency.